The intermediate energy limit is defined by \(l^{\prime }\Lambda _c \ll 1\ll l\Lambda _c\)  or equivalently \(r_c\ll r^*_{l^{\prime }}\)  and \(r^*_{l^{\prime }+2l}\rightarrow r_c\)  which is depicted in figure REF . In this limit, the extremal surface \(\Gamma _{l^{\prime }}\)  is restricted to be near the boundary and the turning point of the extremal surface \(\Gamma _{2l+l^{\prime }}\)  approaches \(r_c\) . Expanding the first and fourth terms in eq.(REF ) up to the second order in \(\frac{r_c}{r^*_{l^{\prime }}}\) , replacing \(r^*_{l^{\prime }}\)  with eq.(REF ) and considering the limit of \(r^*_{l^{\prime }+2l}\rightarrow r_c\)  we reach the following expression

Ep(l'c)4GN(5)Ep(l',l'c)L2c2=1(l'c)22a12+(C2-34(l'c ))(l'c)2-C14(l'c )4,       C1, C2>0,

where \(\hat{E}_p(l^{\prime }\Lambda _c)\)  is the redefined \(E_p(l^{\prime },l^{\prime }\Lambda _c)\)  which is given by eq.(REF ) and \(C_2\)  is a numerical constant given by eq.(REF ) in appendix . As we expect in the limit \(l^{\prime }\Lambda _c \ll 1\ll l\Lambda _c\) , \(\hat{E}_p(l^{\prime }\Lambda _c)\)  does not depend on the length of the subsystems \(l\)  which is coincides with [1]}, [2]}. The first term is the leading term diverges in the limit \(l^{\prime }\rightarrow 0\) , where the two subsystems touch each other. The other two terms indicate the non-conformal effects which are always positive and hence the non-conformality increases \(\hat{E}_p(l^{\prime }\Lambda _c)\) . From eq.(REF ) we observe that \(\hat{E}_p(l^{\prime }\Lambda _c)\)  decrease by increasing \(l^{\prime }\Lambda _c \) .
